带电涡旋的静电透镜
Electrostatic lens of a charged vortex
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中文总结 AI 辅助
该研究探究带电超流体柱对称涡旋的局域静电响应，通过Popov作用量推导标量势近轴展开式，明确各阶系数，分解出态方程贡献，建立涡旋芯热力学与静电分布的解析联系。
中文摘要 AI 辅助
我们研究带电超流体在柱对称涡旋存在下的局域静电响应，其中粒子密度和热力学压缩率均可随径向坐标变化。从仅含相位的Popov作用量得到的静电电荷响应出发，我们引入局域密度扩展并推导标量势的近轴正则展开式，明确得到常数项、二次项和四次项系数，其表达式依赖于局域屏蔽响应及涡旋密度分布的主导非均匀贡献。对于三维幺正费米态方程，压缩率的密度依赖性会对四次项系数产生确定的热力学贡献，所得分解将该态方程贡献与同阶出现的普通常数屏蔽项、电荷源项区分开，为涡旋芯热力学与带电超流体的局域静电分布提供了简洁的解析联系。
英文摘要
We study the local electrostatic response of a charged superfluid in the presence of a cylindrically symmetric vortex, allowing both the particle density and the thermodynamic compressibility to vary with the radial coordinate. Starting from the electrostatic charge response obtained from the phase-only Popov action, we introduce a local-density extension and derive the regular near-axis expansion of the scalar potential. The constant, quadratic, and quartic coefficients are obtained explicitly in terms of the local screening response and of the leading nonuniform contribution to the vortex density profile. For a three-dimensional unitary Fermi equation of state, the density dependence of the compressibility generates a definite thermodynamic contribution to the quartic coefficient. The resulting decomposition separates this equation-of-state contribution from the ordinary constant-screening and charge-source terms that occur at the same order. This provides a compact analytical connection between vortex-core thermodynamics and the local electrostatic profile of a charged superfluid.
